While I do not agree that the Gita is many thousands
of years old (about 2500 or a little less seems right),
Phulgenda Sinha's work is a farce. He ignores nearly
all textual research into the historical Gita, completely
misunderstands key philosophical concepts, and is purely
interested in attacking Vedanta. I read his book and
found his methodology extremely lacking. Try to look
up footnotes which corroborate his statements!

He also lies a great deal. His statements about Al-beruni,
for example, are complete fabrications.